- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# How to measure low resistances? (Resistance Measurement Methods)

The resistances of the values of *less than or equal to *1 Ω are classified as** low resistances**. For example, the resistances of armatures and series windings of large machines, ammeter shunts, contacts, etc.

## Measurement of Low Resistances

For the measurement of low resistances, the following methods are used −

Ammeter-Voltmeter Method

Potentiometer Method

Kelvin Double Bridge Method

### Ammeter – Voltmeter Method

In this method, current through the unknown resistor (Rx) and the potential drop across it are simultaneously measured. The readings are obtained by ammeter and voltmeters respectively. There are two ways in ammeter and voltmeters may be connected for measurement as,

**Case 1** – When voltmeter is directly connected across the resistor, then the ammeter measures current flowing through the unknown resistance (R_{x}) and the voltmeter.

Current through ammeter = Current through(𝑅_{x}) + Current through voltmeter

$$\mathrm{I=I_{R_{x}}+I_{V}}$$

$$\mathrm{\Rightarrow\:I_{R_{x}}=I-I_{V}}$$

Therefore, the value of unknown resistance,

$$\mathrm{R_{x}=\frac{V}{I_{x}}=\frac{V}{I-I_{V}}=\frac{V}{I-(V/R_{V})}\:\:\:...(1)}$$

**Case 2** – When the ammeter is connected such that it measures only the current flowing through the unknown resistor (R_{x}), then the voltmeter measures voltage drop across the ammeter and R_{x}.

Therefore,

$$\mathrm{V=IR_{A}+IR_{x}=l(R_{A}+R_{x})}$$

$$\mathrm{\Rightarrow\:R_{x}=\frac{V}{l}-R_{A}\:\:\:...(2)}$$

### Potentiometer Method

In the *potentiometer method,* the unknown resistance is compared with a standard resistance of the same order of magnitude.

The circuit consists of an unknown resistance (R_{x}), a rheostat (R) and a standard resistance (R_{s}) all are connected in series across a low voltage, high current supply. The value of Rs should be known and of the same order of R_{x}. The current flowing in the circuit is adjusted,so that the potential difference across each resistor is about 1 V.

Now, the voltage drop across both the standard resistance (R_{s}) and unknown resistance (R_{x}) are measured by a potentiometer. The ratio of the two potentiometer readings gives the ratio of R_{x} and R_{s}, i.e.

$$\mathrm{\frac{R_{x}}{R_{s}}=\frac{V_{R_{x}}}{V_{R_{s}}}\:\:\:\:...(3)}$$

### Kelvin Double Bridge Method

The *Kelvin double bridge* is a modified version of Wheatstone bridge and used to measure the low resistances with higher accuracy. This bridge is called double bridge since the circuit contains a second set of ratio arms (*p* and *q*). This second set of ratio arms connects the galvanometer (G) to a point f at the appropriate potential difference between c and d and this eliminates the effect of yoke resistance r. The galvanometer shows zero reading when potential at a equals to the potential at f, i.e. the bridge is balanced.

Therefore, the value of unknown resistance can be given by,

$$\mathrm{R_{x}=\frac{PS}{Q}+\frac{pr}{p+q+r}(\frac{P}{Q}-\frac{p}{q})}$$

Since, the ratio of resistances of arms p and q is the same as the ratio of P and Q. Thus,

$$\mathrm{\frac{p}{q}=\frac{P}{Q}}$$

Substituting in the above expression, we get,

$$\mathrm{R_{x}=\frac{PS}{Q}\:\:\:...(4)}$$

The eq. (4) is the work equation of kelvin double bridge.

- Related Articles
- How to measure high resistances? (Resistance Measurement Methods)
- How to measure medium resistances? (Resistance Measurement Methods)
- Electrical Resistance and Resistivity – Definition, Formula, Unit and Measurement
- Mention the measurement units of length which can measure less than mm.
- What is Voltage – Definition, Formula, Unit, Types and Methods of Measurement
- Low level difference between Slice and Splice methods in Javascript
- How is measurement expressed?
- Time Measurement
- How to define a measurement in screen pixels with CSS?
- How to set font size using CSS Measurement Unit vmin?
- CSS Measurement Units
- What is measurement?
- Standard Measurement Units
- Measurement of Attitude
- Measurement of Interests